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Glossary
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StatisticsIntroduction
Reading time: ~10 min
At the school mela, Riya's class ran a pani-puri stall with a challenge: eat as many as you can in one go. Eleven friends took it on, and Riya noted down every score:
1, 2, 2, 2, 3, 4, 5, 7, 9, 10, 10
The next day the class teacher asked, "So how many pani-puris does a typical student eat?" Aman said 5. Kabir said 4. Riya said 2. All three were sure, and all three could back up their answer.
Here are the eleven friends as grey counters on a plank, each one placed above the number of pani-puris they ate.
Slide the pivot under the plank and complete all three missions.
Pivot under ${p} pani-puris
So nobody was wrong — they simply meant different things by "typical". Aman's 5 is the mean: the point where the whole list balances. Kabir's 4 is the median: the friend in the middle when everyone lines up in order. Riya's 2 is the mode: the score that turns up most often. Each of them replaces a whole list by a number that speaks for the group, and so all three are called measures of central tendency. In this chapter the mean is always drawn in blue, the median in green and the mode in purple.
In Class IX you sorted data into ungrouped and grouped frequency distributions, drew bar graphs, histograms and frequency polygons, and found the mean, median and mode of ungrouped lists like Riya's, where every single value is known. Real data is rarely like that. A board result covers lakhs of students, so it is published in groups — "so many students scored between 40 and 50" — and the individual marks are lost. This chapter carries all three measures over to such grouped data. Along the way you will meet cumulative frequency, a running total that turns out to be the key to the median.