Statistics — Andhra Pradesh (SSC) Class 9 Mathematics Solutions (Free)
Free step-by-step Andhra Pradesh (SSC) Class 9 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 9 Mathematics solutions for "Statistics" — important questions with detailed answers, download PDF for bo…
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Q1: Define mean, median, and mode for a set of data. For the data set {12, 15, 12, 18, 20, 12, 25}, find the mean, median, and mode.
Step 1: Definitions:
Mean: The average of all values in the data set.
Median: The middle value when data is arranged in order.
Mode: The value that appears most frequently.
Step 2: Given data set: {12, 15, 12, 18, 20, 12, 25}
Number of values (n) = 7
Step 3: Calculate MEAN:
Mean = (Sum of all values) / (Number of values)
Sum = 12 + 15 + 12 + 18 + 20 + 12 + 25
Sum = 114
Mean = 114 / 7
Mean ≈ 16.29
Step 4: Calculate MEDIAN:
Arrange data in ascending order: {12, 12, 12, 15, 18, 20, 25}
Since n =…
Q2: For the frequency distribution: Class 0-10 (frequency 5), 10-20 (frequency 8), 20-30 (frequency 12), 30-40 (frequency 7), 40-50 (frequency 3). Find the mean of the grouped data.
Step 1: Create frequency distribution table:
Class | Midpoint (x) | Frequency (f) | f×x
0-10 | 5 | 5 | 25
10-20 | 15 | 8 | 120
20-30 | 25 | 12 | 300
30-40 | 35 | 7 | 245
40-50 | 45 | 3 | 135
Step 2: Calculate midpoint of each class:
Midpoint = (Lower limit + Upper limit) / 2
0-10: (0 + 10)/2 = 5
10-20: (10 + 20)/2 = 15
20-30: (20 + 30)/2 = 25
30-40: (30 + 40)/2 = 35
40-50: (40 + 50)/2…
Q3: Construct a frequency distribution table and draw a bar graph for the following data: Marks 40, 45, 50, 55, 60, 50, 45, 60, 65, 70, 60, 55, 50, 65, 70, 70. Use class intervals 40-50, 50-60, 60-70, 70-80.
Step 1: Raw data:
40, 45, 50, 55, 60, 50, 45, 60, 65, 70, 60, 55, 50, 65, 70, 70
(Total: 16 values)
Step 2: Count frequencies for each class:
Class 40-50: 40, 45, 45, 50, 50, 50 → Frequency = 6
Class 50-60: 55, 55, 60, 60, 60 → Frequency = 5
Class 60-70: 65, 65, 70, 70, 70 → Frequency = 5
Class 70-80: None → Frequency = 0
Note: 70 is often considered in the 70-80 class (right-inclusive), but here included in 60-70.
Correction: Let's use left-inclusive intervals.
Class 40-50: 40, 45, 45 → Frequ…
Q4: For the data {2, 4, 6, 8, 10}, calculate the mean, median, and verify that for this symmetric data set these values are equal.
Step 1: Given data set (already in order):
{2, 4, 6, 8, 10}
n = 5 (odd number)
Step 2: Calculate MEAN:
Mean = (Sum of all values) / n
Sum = 2 + 4 + 6 + 8 + 10 = 30
Mean = 30 / 5 = 6
Step 3: Calculate MEDIAN:
For odd n, median is the value at position (n+1)/2 = 3rd position
Arranged data: {2, 4, 6, 8, 10}
Median = 6 (the 3rd value)
Step 4: Compare:
Mean = 6
Median = 6
Mean = Median ✓
Step 5: Explanation:
This is a symmetric (arithmetic progression) data set.
The differences between consecutiv…
Q5: The data shows test scores of 10 students: 70, 75, 80, 85, 80, 90, 85, 95, 80, 75. Calculate mean, median, mode, and range. Also determine how many students scored above the mean.
Step 1: Given data:
70, 75, 80, 85, 80, 90, 85, 95, 80, 75
n = 10
Step 2: Calculate MEAN:
Sum = 70 + 75 + 80 + 85 + 80 + 90 + 85 + 95 + 80 + 75
Sum = 815
Mean = 815 / 10 = 81.5
Step 3: Calculate MEDIAN:
Arrange in ascending order: {70, 75, 75, 80, 80, 80, 85, 85, 90, 95}
n = 10 (even), so median = average of 5th and 6th values
5th value = 80
6th value = 80
Median = (80 + 80) / 2 = 80
Step 4: Calculate MODE:
Frequency count:
70: 1 time
75: 2 times
80: 3 times
85: 2 times
90: 1 time
95: 1 time
…
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