Statistics Notes: Class 10 Maths Chapter 13
Class 10 Maths Chapter 13 Statistics covers finding the mean, median and mode of grouped data, and the concept of the cumulative frequency curve (ogive).
Overview of Topics & Subtopics (Click to Jump)
1. Mean of Grouped Data
Short Note:
• Direct Method: Mean = Σfixi / Σfi, where xi are class marks and fi are frequencies.
• Assumed Mean Method: Mean = a + (Σfidi / Σfi), where di = xi − a (a = assumed mean).
• Step-Deviation Method: Mean = a + [(Σfiui / Σfi) × h], where ui = (xi−a)/h.
2. Mode of Grouped Data
Short Note:
• Mode = l + [(f1−f0) / (2f1−f0−f2)] × h, where l = lower limit of modal class, f1 = frequency of modal class, f0 = frequency of class preceding it, f2 = frequency of class succeeding it, h = class width.
3. Median of Grouped Data
Short Note:
• Median = l + [(n/2 − cf) / f] × h, where l = lower limit of median class, n = total frequency, cf = cumulative frequency of class preceding median class, f = frequency of median class, h = class width.
4. Graphical Representation (Ogive)
Short Note:
• A cumulative frequency curve (ogive) can be drawn as 'less than' type or 'more than' type; the x-coordinate of the intersection of both ogives gives the median of the data.
NCERT Textbook Exercise Questions
Find the mean of the following distribution using the direct method: Classes 0-10,10-20,20-30 with frequencies 7,10,13 (assume mid-values 5,15,25).
Answer: Σfixi = 7×5 + 10×15 + 13×25 = 35+150+325 = 510. Σfi = 30. Mean = 510/30 = 17.
The following distribution shows the daily pocket allowance of children. If the mean is Rs 18, find the missing frequency f.
Answer: Using Mean = Σfixi/Σfi = 18 and setting up the equation with the missing frequency f as an unknown in the total, solving the resulting linear equation gives the value of f (this requires the specific class data from the textbook table to compute numerically).
Find the mode of the data: classes 10-20,20-30,30-40,40-50 with frequencies 5,8,12,6, where the modal class is 30-40.
Answer: l=30, f1=12, f0=8, f2=6, h=10. Mode = 30 + [(12−8)/(2×12−8−6)] × 10 = 30 + (4/10)×10 = 34.
The median of the following data is 525. Find the values of x and y, if the total frequency is 100 (as per the standard NCERT table).
Answer: Using the median formula with the median class identified from cumulative frequencies, and the condition that all frequencies sum to 100, two simultaneous linear equations are formed and solved to get the values of x and y.
