An engineer collected the following data from a lab...

An engineer collected the following data from a lab experiment: 73 79 89 83 87 76 86 86 77 99 113 89 104 102 89 92 116 91 85 83 94 106 88 79 78 88 a) Complete the frequency distribution table using the class intervals below: CLASS Mid Frequency Value 70-79 80-89 90-99 100-109 110-119 Relative Frequency Cumulative Relative Frequency b) Construct a relative frequency curve. Compare with a bell-shaped curve. c) Sketch the cumulative distribution curve and label the curve with values of the median, Q1, and the 90th percentile. d) Calculate the mean, standard deviation and coefficient of variation using the frequency distribution of the grouped data. e) Construct a Stem-and Leaf diagram.

Transcript

00:01 All right, so i see that you need help with this problem.

00:03 And so the first thing that i did was i put the numbers in order from least to greatest, so that way i could fill out the frequency distribution table.

00:13 So the first thing i need to do is i need to find the mid value.

00:16 That's the number that's in between 70 to 79.

00:18 So you can add the two numbers together, divide by two, and you would get 74 .5.

00:24 Then 80 to 89 would be 84 .5.

00:27 Then 90 to 99 would be 94 .5.

00:32 100 to 109 would be 104 .5.

00:37 110 to 119 would be 114 .5.

00:41 Then as far as the frequency goes, from 70 to 79, there's six.

00:51 Then from 80 to 89, there's 1 ,29, there's 1 ,2, 3, 4, 4.

00:58 5, 6, 7, 8, 9, 10, 11.

01:03 Then from 90 to 99, that's this money, that's 4.

01:13 Then from 100 to 109, there's 3.

01:20 Then from 110 to 119, there's 2.

01:23 Then to find the relative frequency is there is a total of 26 numbers.

01:28 So i'm going to do 6 divided by 26, 11 divided by, 26, 4 divided by 26, 3 divided by 26, and then 2 divided by 26.

01:45 Okay, so 6 divided by 26 is 0 .23, 11 divided by 26 is 0 .42, 4 divided by 26 is 0 .15, and 3 divided by 26 is 0 .12.

01:58 2 .2.

01:58 2 divided by 26 is 0 .08.

02:01 Then for the cumulative relative to frequency, you're adding up all of these.

02:06 So the first one is 0 .23.

02:08 Then 0 .23 plus 0 .42 is 0 .65.

02:14 Then i'm going to add 0 .15 to 0 .65, which would be 0 .80.

02:22 And then adding in 0 .12, which would be 0 .92, and then adding 0 .02, and then adding 0 .08, which would be 1 .02, and then adding 0 .08, which would be 1 .00.

02:33 And so then what i did was i'm going to replace this with an excel sheet so that it's a little bit neater for you to see.

02:43 Okay, so then here it is the excel spreadsheet that i created so that you can see the numbers a lot clearer.

02:51 Then the next question asks, construct a relative frequency curve compare with a bell shape curve.

03:00 So what i'm going to do next is i will insert the relative frequency curve that i did create with this table.

03:12 Okay, so here is my relative frequency curve and compare with the bell shape curve.

03:19 So this is definitely skewed right.

03:23 So i'm going to write that down...

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