The results of 58 test scores for a 9th grade math test are...

Name: the results of 58 test scores for a 9th grade math test are given below 10 10 11 13 15 16 16 17 17 17 18 18 18 18 18 19 20 20 24 25 25 26 26 26 27 27 27 27 27 28 29 32 34 34 36 36 36 36 37 3 40039
Uploaded: 2023-06-27T15:05:17-08:00
Duration: 6 min 11 s
Channel: Madhur L
Description: the results of 58 test scores for a 9th grade math test are given below 10 10 11 13 15 16 16 17 17 17 18 18 18 18 18 19 20 20 24 25 25 26 26 26 27 27 27 27 27 28 29 32 34 34 36 36 36 36 37 3 40039

The results of 58 test scores for a 9th grade math test are given below. 10 10 11 13 15 16 16 17 17 17 18 18 18 18 18 19 20 20 24 25 25 26 26 26 27 27 27 27 27 28 29 32 34 34 36 36 36 36 37 38 39 39 40 40 42 42 46 47 47 48 48 48 48 49 49 49 50 50 Download CSV Find the percentile rank for a student who scored a 17 on the test. percentile Submit Question

Transcript

00:01 Hello students, we have given the scores of 19 students on the math test.

00:07 So sample size n is equal to 19, which is the odd number.

00:11 Then by using this data set, we have to calculate the mean median standard deviation then first quartiles 37th percentile 63rd percentile and 55th percentile.

00:25 So first to calculate the mean we know the formula for the mean is that is x bar which is equal to summation of x divided by n.

00:39 So now this is equal to 8 plus 10 plus 8 plus this is up to 16 plus 15 and divide by the total number of observations that is 19.

00:53 So this is equal to 13 .4737 then we have to calculate the median.

01:02 So to find the median first arrange the data arrange the given data in an ascending order ascending order.

01:21 Now we have n that is sample size which is equal to 19, which is the odd number and when n is odd then the formula for the median is equal to n plus 1 by tooth observation, which is equal to 19 plus 1 divide by tooth observation and that is equal to 10th observation.

01:51 So now after arranging the data in the ascending order, we will get the 10th observation is equal to 14.

01:58 So therefore median is equal to 14.

02:01 Then next we have to calculate the standard deviation and the formula for the standard deviation is standard deviation is equal to summation of x minus x bar bracket square divide by n minus 1 and this whole term is inside the square root sign.

02:20 So we have already calculated the sample mean that is x bar.

02:25 So by using that value we will get the standard deviation is equal to 1 upon n minus 1 that is 18 into bracket 8 minus 13 .4737 bracket square plus this is up to 15 minus 13 .4737 bracket square and this whole term is inside the square root sign.

02:52 So this is equal to 4 .0875.

02:58 This is the standard deviation.

03:00 Then we have to calculate the first quartiles that is q1 and the formula for q1 is q1 is equal to n plus 1 divide by fourth observation.

03:14 So here n is equal to 19...

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