Statistics and Data Handling is a scoring topic in MP TET Mathematics that tests your ability to organise, represent, and interpret numerical data. At the primary and upper-primary levels, this topic focuses on graphical representations (bar graphs, pie charts) and measures of central tendency (mean, median, mode).
Questions typically ask you to read values from graphs, calculate averages, or identify the most frequent data point. Since these concepts connect directly to real-life situations—classroom attendance, crop production, temperature records—examiners often frame problems using practical contexts relevant to Madhya Pradesh.
Mastering this topic requires understanding when to use each measure and how to extract information quickly from visual data. The calculations are straightforward, but careless errors in reading graphs or arranging data cost marks.
Key Concepts
**Data** is a collection of numerical facts or information gathered through observation, survey, or experiment. Raw data must be organised before analysis.
**Bar Graph** uses rectangular bars of equal width to represent data. The height (or length) of each bar shows the value of that category. Bars can be vertical or horizontal and must have equal gaps between them.
**Pie Chart (Circle Graph)** represents data as sectors of a circle. The whole circle (360°) represents the total, and each sector's angle is proportional to its share of the total.
**Mean (Arithmetic Average)** is the sum of all observations divided by the number of observations. It is affected by extreme values (outliers).
**Median** is the middle value when data is arranged in ascending or descending order. For an even number of observations, median is the average of the two middle values.
**Mode** is the observation that occurs most frequently. A data set can have no mode, one mode, or multiple modes.
**Range** is the difference between the highest and lowest values—it measures the spread of data.
**Frequency** tells how many times a particular value appears in the data set.
Formulas / Key Facts
**Mean (Arithmetic Mean)** Mean = Sum of all observations ÷ Number of observations Mean = Σx ÷ n
**Median**
Arrange data in ascending order
If n is odd: Median = value at position (n + 1)/2
If n is even: Median = average of values at positions n/2 and (n/2 + 1)
**Mode** Mode = observation with highest frequency (no formula—just count)
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**Example 5: Pie Chart Calculation** A family's monthly expenditure is ₹20,000. They spend ₹5,000 on food. Find the central angle for food in a pie chart.
**Example 6: Reading a Bar Graph** A bar graph shows rice production (in lakh tonnes): 2018 = 45, 2019 = 52, 2020 = 48. What is the average production over three years?
**Not arranging data before finding median** → Always arrange data in ascending (or descending) order first. Finding the "middle" of unsorted data gives a wrong answer.
**Confusing mean and median** → Mean uses sum and division; median uses position after sorting. For data with extreme values, median better represents the "typical" value.
**Forgetting to average two middle values for even n** → When the count is even, students often pick just one middle value. You must average the two central values.
**Calculating pie chart angle without using 360°** → Some students multiply by 100 (percentage) instead of 360. Central angle calculation always uses 360°.
**Misreading bar graph scale** → Check the scale carefully. If one unit on the y-axis represents 10 (not 1), a bar reaching 4 units means 40, not 4.
**Declaring "no mode" when data has equal frequencies** → If two or more values share the highest frequency, the data is bimodal or multimodal—not "no mode." No mode occurs only when every value appears equally often.
Quick Reference
Mean = Total sum ÷ Number of items
Median: Sort first, then find middle value (average two if even count)
Mode = Most frequent value
Pie chart angle = (Part ÷ Whole) × 360°
Range = Highest − Lowest
Bar graphs: equal bar widths, equal gaps, check axis scale before reading