Bihar Board Class 10 · Maths · Matric exam 2027
Chapter 14: Statistics — notes
The chapter’s 5 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.
1. Mean of Grouped Data - Direct Method
You already know the mean of data is found by adding up all the values and dividing by the number of observations.
- • Mean x = Σfixi / Σfi
- • Class mark = (Upper limit + Lower limit)/2
- • Example: classes 10-25,...,85-100
- • Σfi = 30, Σfixi = 1860.0
- • x = 1860.0/30 = 62
2. Assumed Mean Method and Step-deviation Method
Okay, so sometimes the class marks and frequencies are big numbers.
- • di = xi − a
- • x = a + Σfidi/Σfi
- • ui = (xi − a)/h
- • x = a + h×(Σfiui/Σfi)
- • Example: a = 47.5, h = 15, x = 62
3. Mode of Grouped Data
Okay, so the mode is the value that shows up most often in the data.
- • Mode = l + h×(f1−f0)/(2f1−f0−f2)
- • l = lower limit of modal class
- • h = class size
- • f1 = modal class freq, f0 = preceding, f2 = succeeding
- • Example: l = 40,h = 15,f1 = 7,f0 = 3,f2 = 6
- • Mode = 40+15(4/5) = 52
4. Cumulative Frequency and Median of Grouped Data
Okay, so the median is the middle-most value, once data is arranged in order.
- • Cumulative frequency = sum of frequencies up to a class
- • Median class: cf just greater than n/2
- • Median = l + h×((n/2-cf)/f)
- • Example: n = 53, n/2 = 26.5
- • l = 60,cf = 22,f = 7,h = 10 → Median = 66.4
5. Choosing Mean, Median or Mode & Graphs (Ogives)
Okay, so each of these three — mean, median, mode — suits a different purpose.
- • 3 Median = Mode + 2 Mean
- • Mean: best for overall comparison
- • Median: best for typical value with extremes
- • Mode: best for most frequent value
- • Ogive: cumulative frequency curve
- • Median = x-coordinate where two ogives meet
Summary
Okay, so let's go back over everything we did in this chapter. We started with the mean of grouped data. You saw three ways to find it — the Direct Method, the Assumed Mean Method, and the Step-deviation Method. All three use the class mark to represent each class, and — this is the nice part — all three give you the same answer. Then we moved to mode. For grouped data, you found it using the modal class, along with a formula that uses the frequencies just before and just after that class. After that came cumulative frequency, where you keep adding up frequencies class by class. That idea took us straight to the median formula, which uses the median class. We also talked about why we need all three measures — mean, median and mode. Mean gives you the overall average, median gives you the typical, middle value, and mode gives you the most frequent value. And they're connected too, by 3 Median = Mode + 2 Mean. Finally, you learned to draw ogives — cumulative frequency curves — of the less than type and the more than type. Where those two curves cross, that point gives you the median, graphically. So, out of all these ideas, which one did you find the most interesting?
AskMedha · Medha Ma’am — Bihar Board Class 10 Maths, Chapter 14. Written from the textbook, checked twice.
Questions parents and students ask
- How do I get the "Statistics" notes as a PDF?
- Press "Save as PDF" — the phone’s print sheet opens; choose "Save as PDF" there. The PDF holds the notes only.
- Where are these notes written from?
- From the chapter’s own textbook text, part by part, in the book’s own terms; a second, independent model then checked every part against the book. The full lesson, a check question for each part and the practice are in the AskMedha app.
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