Statistics — Andhra Pradesh (SSC) Class 10 Mathematics Solutions (Free)
Free step-by-step Andhra Pradesh (SSC) Class 10 Mathematics solutions for "Statistics" — important questions with detailed answers, download PDF for board exam preparation.
TL;DR: Free step-by-step Andhra Pradesh (SSC) Class 10 Mathematics solutions for "Statistics" — important questions with detailed answers, download PDF for b…
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Q1: Find the mean of the following grouped data using the assumed mean method: Class Interval: 0-10, 10-20, 20-30, 30-40, 40-50 Frequency: 5, 15, 20, 8, 2
Step 1: Construct the table with class midpoints (x) and deviations (d) from assumed mean 25
Step 2: Assumed mean A = 25 (midpoint of 20-30)
Step 3: Class Intervals and calculations:
0-10: midpoint = 5, d = 5-25 = -20, f = 5, fd = -100
10-20: midpoint = 15, d = 15-25 = -10, f = 15, fd = -150
20-30: midpoint = 25, d = 25-25 = 0, f = 20, fd = 0
30-40: midpoint = 35, d = 35-25 = 10, f = 8, fd = 80
40-50: midpoint = 45, d = 45-25 = 20, f = 2, fd = 40
Step 4: Sum of frequenci…
Q2: Find the median of the following grouped data: Class Interval: 0-5, 5-10, 10-15, 15-20, 20-25 Frequency: 4, 6, 12, 8, 5
Step 1: Find cumulative frequencies
0-5: f = 4, cf = 4
5-10: f = 6, cf = 10
10-15: f = 12, cf = 22
15-20: f = 8, cf = 30
20-25: f = 5, cf = 35
Step 2: Total frequency N = 35
Step 3: N/2 = 35/2 = 17.5
Step 4: Median class is 10-15 (since cf = 22 is just greater than 17.5)
Step 5: Median = L + [(N/2 - cf)/f] × h
Step 6: Here, L = 10 (lower limit of median class), N/2 = 17.5
Step 7: cf = 10 (cumulative frequency before median class)
Step 8: f = 12 (frequency of median class…
Q3: Find the mode of the following grouped data: Class Interval: 10-20, 20-30, 30-40, 40-50, 50-60 Frequency: 3, 7, 12, 8, 5
Step 1: The modal class is the class with the highest frequency
Step 2: Frequencies: 3, 7, 12, 8, 5
Step 3: Modal class is 30-40 (frequency = 12)
Step 4: Mode = L + [(f1 - f0)/(2f1 - f0 - f2)] × h
Step 5: Here, L = 30 (lower limit of modal class)
Step 6: f1 = 12 (frequency of modal class)
Step 7: f0 = 7 (frequency of class before modal class)
Step 8: f2 = 8 (frequency of class after modal class)
Step 9: h = 10 (class width)
Step 10: Mode = 30 + [(12 - 7)/(2(12) - 7 - 8)] × 10
Step 11: Mode = 30 …
Q4: The mean of the following grouped data is 24. Find the missing frequency f: Class Interval: 10-15, 15-20, 20-25, 25-30, 30-35 Frequency: 4, 6, f, 8, 2
Step 1: Set up table with class midpoints
10-15: x = 12.5, f = 4, fx = 50
15-20: x = 17.5, f = 6, fx = 105
20-25: x = 22.5, f = f, fx = 22.5f
25-30: x = 27.5, f = 8, fx = 220
30-35: x = 32.5, f = 2, fx = 65
Step 2: Total frequency = 4 + 6 + f + 8 + 2 = 20 + f
Step 3: Sum of fx = 50 + 105 + 22.5f + 220 + 65 = 440 + 22.5f
Step 4: Mean formula: Mean = Σfx/Σf
Step 5: 24 = (440 + 22.5f)/(20 + f)
Step 6: 24(20 + f) = 440 + 22.5f
Step 7: 480 + 24f = 440 + 22.5f
Step 8: 24f - 22…
Q5: Draw an ogive for the following cumulative frequency distribution and find the median graphically: Class Interval: 0-10, 10-20, 20-30, 30-40, 40-50 Cumulative Frequency: 8, 20, 35, 48, 50
Step 1: For an ogive, plot the upper class limits on x-axis and cumulative frequencies on y-axis
Step 2: Points to plot: (10, 8), (20, 20), (30, 35), (40, 48), (50, 50)
Step 3: Draw a smooth curve through these points
Step 4: To find median graphically: Find N/2 = 50/2 = 25 on y-axis
Step 5: From point (0, 25), draw a horizontal line to meet the ogive
Step 6: From the intersection point, draw a perpendicular to x-axis
Step 7: The point where it meets x-axis gives the median
Step 8: From the plot…
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