what is the mean and the standard deviation of the data in the table given? round your answer to 2 decimal places
value: 4.8, 5.2, 5.4, 5.9, 6.5, 6.6
frequency: 25, 21, 23, 17, 24, 25
Find the mean first = sum of scores/number of scores.
In your case, multiply the values times the frequencies, sum them, and divide by the total frequency.
Subtract each of the scores from the mean and square each difference. (In your case, multiply that square by each frequency.) Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.
To find the mean, you need to calculate the sum of all the values in the table and divide it by the total frequency. Here's how you can do it:
Step 1: Multiply each value in the table by its corresponding frequency.
4.8 * 25 = 120
5.2 * 21 = 109.2
5.4 * 23 = 124.2
5.9 * 17 = 100.3
6.5 * 24 = 156
6.6 * 25 = 165
Step 2: Add up all the results from Step 1 to get the sum of the values multiplied by their frequencies.
120 + 109.2 + 124.2 + 100.3 + 156 + 165 = 774.7
Step 3: Divide the sum from Step 2 by the total frequency.
774.7 / (25 + 21 + 23 + 17 + 24 + 25) = 774.7 / 135 = 5.73 (rounded to 2 decimal places)
So, the mean (average) of the given data is approximately 5.73.
To find the standard deviation, you can use the following steps:
Step 1: Calculate the variance.
a) Subtract the mean (5.73) from each value in the table (4.8, 5.2, 5.4, 5.9, 6.5, 6.6) separately.
4.8 - 5.73 = -0.93
5.2 - 5.73 = -0.53
5.4 - 5.73 = -0.33
5.9 - 5.73 = 0.17
6.5 - 5.73 = 0.77
6.6 - 5.73 = 0.87
b) Square each result from Step 1a.
(-0.93)^2 = 0.8649
(-0.53)^2 = 0.2809
(-0.33)^2 = 0.1089
(0.17)^2 = 0.0289
(0.77)^2 = 0.5929
(0.87)^2 = 0.7569
Step 2: Multiply each squared result from Step 1b by its corresponding frequency.
0.8649 * 25 = 21.6225
0.2809 * 21 = 5.8989
0.1089 * 23 = 2.5037
0.0289 * 17 = 0.4913
0.5929 * 24 = 14.2296
0.7569 * 25 = 18.9225
Step 3: Add up all the results from Step 2 to get the sum of the squared differences multiplied by their frequencies.
21.6225 + 5.8989 + 2.5037 + 0.4913 + 14.2296 + 18.9225 = 63.6685
Step 4: Divide the sum from Step 3 by the total frequency.
63.6685 / (25 + 21 + 23 + 17 + 24 + 25) = 63.6685 / 135 = 0.4727 (rounded to 4 decimal places)
Step 5: Take the square root of the result from Step 4 to find the standard deviation.
√0.4727 ≈ 0.69 (rounded to 2 decimal places)
So, the standard deviation of the given data is approximately 0.69.