STAT 251 Lecture Notes - Lecture 2: Interquartile Range, Central Tendency, Percentile

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tandeer235

4 Jun 2018

School

UBC

Department

Statistics

Course

STAT 251

Professor

Lasantha Wijendra Acharige

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Measures of Center

Mean

The mean is the sum of the observations divided by the

number of observations. Sample mean is

e.g. Number of hours spent studying per week for 5

students are 4, 6, 8, 7, 5.

Find the mean number of hours spent studying/week.

hours

Chapter 1 – Contd...

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Measures of Center

Median

•The median is the midpoint of the observations when they are

ordered from the smallest to the largest (ascending order)

•If the number of observations is:

–Odd : median is the middle observation; i.e. observation

–Even: median is the average of the two middle observations

average of and observations

Example1 : 12, 14 ,15, 17, 20, 24, 24, 27, 29 ; n = 9

Median is the (9+1)/2 th observation , median = 20

Example 2 : 12, 14 ,15, 17, 20, 24, 24, 27, 29, 30 ; n = 10

Median is the 5 th and 6 th observation , median = (20+24)/2 = 22

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Comparing the Mean and Median

When data nearly symmetric mean ≈ median

In a skewed distribution, the mean is farther out in the long tail

than is the median

•When data have long right tail mean > median

•When data have long left tail mean < median

•For skewed distributions the median is preferred because it is

better representative of a typical observation

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Document Summary

The mean is the sum of the observations divided by the number of observations. Sample mean is e. g. number of hours spent studying per week for 5 students are 4, 6, 8, 7, 5. Find the mean number of hours spent studying/week. hours. Median: the median is the midpoint of the observations when they are ordered from the smallest to the largest (ascending order) Odd : median is the middle observation; i. e. observation. Even: median is the average of the two middle observations average of and observations. Example1 : 12, 14 ,15, 17, 20, 24, 24, 27, 29 ; n = 9. Median is the (9+1)/2 th observation , median = 20. Example 2 : 12, 14 ,15, 17, 20, 24, 24, 27, 29, 30 ; n = 10. Median is the 5 th and 6 th observation , median = (20+24)/2 = 22. When data nearly symmetric mean median.

Related Questions

You are studying the affect of financial means on students' average hours of sleep. You have found a reliable study indicating that students that have a job and do not receive financial support from their parents or guardians sleep an average of 5.8 hours per night (excluding weekends) on average (population average).
You decide to test whether or not students who do not work get more sleep per week night on average. You take a sample of 63 students that do not work and live with parents or guardians then you record the number of hours per week night they sleep for a period of 15 weeks (1 semester). You find that the average (mean) hours slept per week night in your sample is 7.2 hours and the standard deviation is 3.9 hours. Assume that average sleeping hours on week nights is normally distributed across students.

Remember to define the null and alternative hypotheses to help you answer the question.

What will the value of the test statistic (z-test) be?
(Round your answer to two decimal places)

amaranthrabbit32

You are interested in how much time students spend on the internet each day. Here are data on the time spent on the internet (in minutes) for a particular day reported by a random sample of 30 students at a large college:

a) Make a histogram of these data. Is the shape symmetric or skewed?

b) Find the 5 number summary and P_65.

c) Find the mean and sample standard deviation.

d) Are there any outliers? Justify your answer.

e) Would it be better to use the mean and standard deviation or the median and IQR to describe the centre and spread of this distribution? why?

ceruleanhedgehog638

1. Matt the Manager wants to estimate the mean wait time for customers to check out in his Mini-Market. He randomly selects 40 customers and determines the mean wait time is 2.7 minutes. Define the following for this exercise:Experimental Unit or Individual: Is the data collected qualitative or quantitative?Variable (x):Population of Interest:Sample:Parameter of Interest:Statistic:Do you expect the parameter and the statistic to be the same value? Explain.Discuss the use of descriptive and inferential statistics in this exercise.Is the variable, x, discrete or continuous?

2. Identify the populationand samplefor the following examples:a)The P.E. Coach of a middle school interested in the mean height for the 7thgraders in the school. He randomly selects 40 7thgraders and measures the height of each.Population: 7thgraders Sample: 40 7thgraders chosenb)A community college notices that an increasing number of full-time students are working while attending school. The administration randomly selects 200 students and determines how may hours per week each students works.

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STAT 251 Lecture Notes - Lecture 2: Interquartile Range, Central Tendency, Percentile

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