The following data shows the mark of 39 students in an examination. 41 52 37 56 63 48 65 46 54 32 51 66 74 23 35 61 58 44 49 53 45 57 56 38 59 28 50 49 67 56 36 45 79 68 43 56 26 47 55
1) Form a grouped frequency table with the class intervals 20-29, 30-39
2)Find the mean and standard deviation of the distribution
1) Grouped frequency table:
| Class Interval | Frequency |
|----------------|-----------|
| 20-29 | 3 |
| 30-39 | 5 |
| 40-49 | 7 |
| 50-59 | 11 |
| 60-69 | 8 |
| 70-79 | 5 |
2) Mean calculation:
Mean = (Sum of all values) / (Total number of values)
Mean = (41+52+37+56+63+48+65+46+54+32+51+66+74+23+35+61+58+44+49+53+45+57+56+38+59+28+50+49+67+56+36+45+79+68+43+56+26+47+55) / 39
Mean = 1592 / 39
Mean = 40.821
Standard deviation calculation:
Step 1: Find the mean of the data:
Mean = 40.821
Step 2: Find the squared difference from the mean for each value:
(41 - 40.821)^2 = 0.033
(52 - 40.821)^2 = 126.548
(37 - 40.821)^2 = 14.987
.
.
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Step 3: Find the sum of all squared differences:
Sum = 2340.719
Step 4: Divide the sum by the total number of values to find the variance:
Variance = 2340.719 / 39
Variance = 60.010
Step 5: Find the square root of the variance to get the standard deviation:
Standard deviation = sqrt(60.010)
Standard deviation ≈ 7.75
Therefore, the mean of the distribution is 40.821 and the standard deviation is approximately 7.75.