How much sleep do you get on a typical school night? A sample of 10 university students were asked to report the number of hours that they slept on the previous night with the following results: 20 7, 6, 7.25, 7, 8.5, 5, 8, 7, 6.75, 6 a. Find the mean, median, and the standard deviation of the number of hours of sleep for these 10 students. b. Calculate the z-score for the largest value (x = 8.5). Is this an unusually sleepy college student? (Hint: Detection of Outlier using z-score) c. What is the most frequently reported measurement? What is the name for this measure of centre?
here it is given that A group of 10 college students were asked to report the number of hours that they slept on the previous night. With the following regionals X. is equal to seven. It is given the X. is equal to seven six. seven 8.5 white age seven 6.75 N six. Mhm. Mhm. We're external number of hours sleeves. Now we will find question # eight. Mean of X is equal to mean of X difficult to one by Yeah. Okay. And some medicine and article 21 X I. This is equal to seven plus six plus seven point 25-plus 7 plus eight plus 8.5 plus five plus eight plus seven plus 6.75 plus six. Do I read by 10 calculating this will get 68.5 divided by 10. Which is equal to 6.85 cents min is 6.85. Now we will calculate the standard division. Mhm. Yeah. Now we'll calculate. And the standard deviation. Yeah. Yeah. Yeah. No. The formula for standard division age some medicine in I called to one X. I square Yeah. Yeah. Yeah. This is equal to yeah, 70 square plus 60 square plus 7.25. Yeah. Is square Plus 70 square plus 8.55. Only square plus 80 square plus 70 square plus 6.75 squared plus six. Is where Solving this? We will get 478-13 75. No S. X. That is gender division equal to the square root under the square root of one by end -1. Some medicine and I equal to one X. I Squire minus one by N. And minus one into submission. And I called the one ex II. Holy square so this is equal to. Yeah. Mhm. Yes I think this is equal to and that is square root one by 10 minus one 4781375. We have calculated about the value of some S. N. N. I. Equal to one. Xie square equal to 478.375 and -1 x 10 into 10 -1. The value of X. I. Hollis very 68.5 in the square solving this we will get 1.0083 Hands. The Standard Division is 1.03. Now we will solve part B. For the value of X. equal to 8.5. Judges score is given as X minus X. Were divided by S. X. Essex means Eastern Division. So the value of X. is 8.5 -9.85. Thank you divided by one point double 083. So the following this we will get 1.64. Since the value of judges score is not too small. The value of example 285 region and not an Israel sleepy college student since yeah value of jade is not too small. The value Mexico to 8.5. He's not unusually tracking. Okay sleepy. Yes. College student. Oh, thank you. Now we will solve part C. Mhm. Yeah. Yeah. The most frequent reported measurement 87. The most frequent clear. Well here. Think. Of course. Yeah, reported. Mhm. Measurement reports. Mhm. Age seven. Because this measurement reported. Yeah. More than remaining measurement. The name for this measure of center age. The name for this measure of Yeah. Yeah. Center age mode. Hence this is the answer. Yeah. Thank you.