Studdy AI Logo
Math  /  Data & Statistics

Questionللمفرادات التالية 1,7,12,2,5,17,20,15,16,18,1,4,3,7,9
اوجد : 1.المدى Range
3. الاتحراف المعياري Standard Deviation؟

Studdy Solution

STEP 1

1. The data set is: 1,7,12,2,5,17,20,15,16,18,1,4,3,7,9 1, 7, 12, 2, 5, 17, 20, 15, 16, 18, 1, 4, 3, 7, 9 .
2. The range is the difference between the maximum and minimum values.
3. The standard deviation measures the amount of variation or dispersion in a set of values.

STEP 2

1. Calculate the range.
2. Calculate the standard deviation.

STEP 3

Identify the minimum and maximum values in the data set.
Minimum value: 1 1
Maximum value: 20 20

STEP 4

Calculate the range by subtracting the minimum value from the maximum value.
Range=20−1=19 \text{Range} = 20 - 1 = 19

STEP 5

Calculate the mean (average) of the data set.
Sum of data points: 1+7+12+2+5+17+20+15+16+18+1+4+3+7+9=137 1 + 7 + 12 + 2 + 5 + 17 + 20 + 15 + 16 + 18 + 1 + 4 + 3 + 7 + 9 = 137
Number of data points: 15 15
Mean: 13715≈9.13 \frac{137}{15} \approx 9.13

STEP 6

Calculate the variance by finding the average of the squared differences from the mean.
1. Subtract the mean from each data point and square the result.
2. Sum these squared differences.
3. Divide by the number of data points.
Squared differences: (1−9.13)2,(7−9.13)2,(12−9.13)2,(2−9.13)2,(5−9.13)2,(17−9.13)2,(20−9.13)2,(15−9.13)2,(16−9.13)2,(18−9.13)2,(1−9.13)2,(4−9.13)2,(3−9.13)2,(7−9.13)2,(9−9.13)2(1 - 9.13)^2, (7 - 9.13)^2, (12 - 9.13)^2, (2 - 9.13)^2, (5 - 9.13)^2, (17 - 9.13)^2, (20 - 9.13)^2, (15 - 9.13)^2, (16 - 9.13)^2, (18 - 9.13)^2, (1 - 9.13)^2, (4 - 9.13)^2, (3 - 9.13)^2, (7 - 9.13)^2, (9 - 9.13)^2
Sum of squared differences: 8.132+2.132+2.872+7.132+4.132+7.872+10.872+5.872+6.872+8.872+8.132+5.132+6.132+2.132+0.132≈272.67 8.13^2 + 2.13^2 + 2.87^2 + 7.13^2 + 4.13^2 + 7.87^2 + 10.87^2 + 5.87^2 + 6.87^2 + 8.87^2 + 8.13^2 + 5.13^2 + 6.13^2 + 2.13^2 + 0.13^2 \approx 272.67
Variance: 272.6715≈18.18 \frac{272.67}{15} \approx 18.18

STEP 7

Calculate the standard deviation by taking the square root of the variance.
Standard Deviation≈18.18≈4.26 \text{Standard Deviation} \approx \sqrt{18.18} \approx 4.26
The range is:
19 \boxed{19}
The standard deviation is:
4.26 \boxed{4.26}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord