Chapter Hub
Statistics
Statistics in Class 10 focuses on organising data, finding measures of central tendency, and interpreting results clearly. You must know how to handle grouped data, because board questions often give class intervals and frequency tables instead of raw values. This chapter also connects calculation with reading tables and graphs. A good answer should show the correct formula, the correct class, the correct cumulative frequency, and the correct interpretation, especially for mean, median, mode, and ogives.
Difficulty
Medium
Study time
96-120 min
Plan by time
Pick the window that matches what you have right now.
If you have 15 min
Last-pass revision
Skim the Quick Revision table — definitions, formulas, and the traps board examiners reuse.
Open Quick RevisionIf you have 45 min
Targeted practice
Read the high-priority concepts, then take the chapter MCQ quiz to find weak spots.
Start MCQ QuizIf you have 96 min
First full pass
Walk every concept in chapter order, then revise and quiz. Best for the first time you study this chapter.
Open Key ConceptsChapter Learning Map
Start with one of the buckets below, then open the full map when you want the complete concept roadmap.
Means
Covers Mean of grouped data, Assumed mean method and Step deviation method.
Open mapMedian
Covers Median of grouped data and Median from ogive.
Open mapMode
Covers Modal class and Mode of grouped data.
Open mapCumulative Frequency
Covers Cumulative frequency and Less-than cumulative frequency table.
Open mapGraph and Choice
Covers Ogive interpretation, Choice of class mark and Comparing central tendency measures.
Open mapKey Concepts
Concepts grouped the way the chapter is taught — open the group that matches what you want to revise.
Means
Covers Mean of grouped data, Assumed mean method and Step deviation method.
Mean of grouped data
The mean of grouped data is the average value found by using class marks and frequencies of the grouped table.
Assumed mean method
The assumed mean method is a shortcut for finding the mean of grouped data by taking one convenient central value as a reference.
Step deviation method
The step deviation method is a fast way to find the mean of grouped data when class widths are equal.
Median
Covers Median of grouped data and Median from ogive.
Median of grouped data
The median of grouped data is the middle value that divides the frequency distribution into two equal parts.
Median from ogive
The median from an ogive is found by using the total frequency, locating N/2 on the cumulative frequency axis, and reading the corresponding class boundary value.
Mode
Covers Modal class and Mode of grouped data.
Modal class
The modal class is the class interval with the highest frequency in grouped data.
Mode of grouped data
The mode of grouped data is the value that occurs most frequently, estimated using the modal class and a standard formula.
Cumulative Frequency
Covers Cumulative frequency and Less-than cumulative frequency table.
Cumulative frequency
Cumulative frequency is the running total of frequencies up to a class interval.
Less-than cumulative frequency table
A less-than cumulative frequency table lists the number of observations less than each upper class boundary.
Graph and Choice
Covers Ogive interpretation, Choice of class mark and Comparing central tendency measures.
Ogive interpretation
An ogive is a cumulative frequency graph used to interpret grouped data and locate values such as the median.
Choice of class mark
The class mark is the midpoint of a class interval and is used as the representative value of that class in grouped-data calculations.
Comparing central tendency measures
Comparing central tendency measures means deciding whether mean, median, or mode best describes a data set for a given situation.
Exam Intelligence
The traps that cost marks in this chapter, and how its main concepts turn up in the paper.
High Probability Topics
- Mean of grouped data
- Assumed mean method
- Step deviation method
- Median of grouped data
- Modal class
- Mode of grouped data
- Cumulative frequency
- Less-than cumulative frequency table
Common Traps
- Using class limits instead of class marks in mean calculations.
- Forgetting to add the assumed mean back after using the shortcut method.
- Using the modal class as the mode itself in grouped data.
- Writing cumulative frequency as repeated frequency instead of running total.
- Using ordinary frequency points on an ogive instead of cumulative frequencies.
- Choosing mean automatically when the data has extreme values.
How CBSE Asks This Chapter
- Mean of grouped data
Board questions usually give a grouped table and ask for the mean, sometimes asking for a comparison after calculation.
- Assumed mean method
Questions often ask students to find mean using the assumed mean method for a grouped frequency table.
- Step deviation method
Students may be asked to compute the mean of a long grouped table using coded deviations and a common class width.
- Median of grouped data
Questions usually give grouped data and ask for the median using cumulative frequency and the standard median formula.
Quick Revision
Concept, formula or equation to remember, and the trap that loses marks — in one scannable view.
Remember
Mean = Σ(fi xi) / Σfi, where xi is the class mark and fi is the frequency.Trap to avoid
Students often use class intervals directly instead of class marks, which gives an incorrect mean.
Remember
Mean = A + [Σfi di / Σfi], where A is assumed mean and di = xi - A.Trap to avoid
Students forget to add the assumed mean back at the final stage, so the answer becomes incomplete.
Remember
Mean = A + [Σfi ui / Σfi] x h, where ui = (xi - A)/h and h is class width.Trap to avoid
Students forget that this method works best when all class widths are equal, so they apply it blindly to unequal intervals.
Remember
Median = l + [(N/2 - cf) / f] x h, where l is lower boundary, cf is cumulative frequency before median class, f is frequency of median class, and h is class width.Trap to avoid
Students often choose the class with the highest frequency instead of the class containing the middle position.
Remember
Modal class = the class interval with maximum frequency; it is used in the grouped-data mode formula.Trap to avoid
Students sometimes choose the class with the widest interval instead of the class with the highest frequency.
Remember
Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] x h, where l is lower boundary of modal class, f1 is modal class frequency, f0 is preceding frequency, f2 is succeeding frequency, and h is class width.Trap to avoid
Students often use the frequency of the modal class as the mode itself, which is not correct for grouped data.
Remember
Cumulative frequency of a class = sum of its frequency and all previous frequencies.Trap to avoid
Students sometimes write each class frequency again instead of adding them cumulatively.
Less-than cumulative frequency table
Remember
Less-than cumulative frequency = running total of frequencies written against upper class boundaries.Trap to avoid
Students sometimes attach the cumulative total to the lower boundary instead of the upper boundary.
Remember
Ogive points are formed by plotting cumulative frequency against upper class boundaries for less-than ogive.Trap to avoid
Students often plot ordinary frequencies on an ogive instead of cumulative frequencies.
Remember
Median from ogive is read at the x-value corresponding to N/2 on the y-axis of the less-than curve.Trap to avoid
Students sometimes read the median from the wrong axis or forget to use half of the total frequency.
Remember
Class mark = (lower limit + upper limit) / 2.Trap to avoid
Students sometimes choose the upper limit or lower limit instead of the midpoint.
Comparing central tendency measures
Remember
Mean uses all values, median uses the middle position, and mode uses the most frequent value.Trap to avoid
Students often pick the mean for every data set without checking whether the data has extreme values.
| Concept | Remember | Trap to avoid |
|---|---|---|
| Mean of grouped data | Mean = Σ(fi xi) / Σfi, where xi is the class mark and fi is the frequency. | Students often use class intervals directly instead of class marks, which gives an incorrect mean. |
| Assumed mean method | Mean = A + [Σfi di / Σfi], where A is assumed mean and di = xi - A. | Students forget to add the assumed mean back at the final stage, so the answer becomes incomplete. |
| Step deviation method | Mean = A + [Σfi ui / Σfi] x h, where ui = (xi - A)/h and h is class width. | Students forget that this method works best when all class widths are equal, so they apply it blindly to unequal intervals. |
| Median of grouped data | Median = l + [(N/2 - cf) / f] x h, where l is lower boundary, cf is cumulative frequency before median class, f is frequency of median class, and h is class width. | Students often choose the class with the highest frequency instead of the class containing the middle position. |
| Modal class | Modal class = the class interval with maximum frequency; it is used in the grouped-data mode formula. | Students sometimes choose the class with the widest interval instead of the class with the highest frequency. |
| Mode of grouped data | Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] x h, where l is lower boundary of modal class, f1 is modal class frequency, f0 is preceding frequency, f2 is succeeding frequency, and h is class width. | Students often use the frequency of the modal class as the mode itself, which is not correct for grouped data. |
| Cumulative frequency | Cumulative frequency of a class = sum of its frequency and all previous frequencies. | Students sometimes write each class frequency again instead of adding them cumulatively. |
| Less-than cumulative frequency table | Less-than cumulative frequency = running total of frequencies written against upper class boundaries. | Students sometimes attach the cumulative total to the lower boundary instead of the upper boundary. |
| Ogive interpretation | Ogive points are formed by plotting cumulative frequency against upper class boundaries for less-than ogive. | Students often plot ordinary frequencies on an ogive instead of cumulative frequencies. |
| Median from ogive | Median from ogive is read at the x-value corresponding to N/2 on the y-axis of the less-than curve. | Students sometimes read the median from the wrong axis or forget to use half of the total frequency. |
| Choice of class mark | Class mark = (lower limit + upper limit) / 2. | Students sometimes choose the upper limit or lower limit instead of the midpoint. |
| Comparing central tendency measures | Mean uses all values, median uses the middle position, and mode uses the most frequent value. | Students often pick the mean for every data set without checking whether the data has extreme values. |
Practice
Use short concept checks first, then move into the full chapter test.
Free Chapter MCQ Quiz
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