Multiple Choice Exercise

*** Choose one answer and click [Submit] button

4.1 Which of the following data is an average of 28, a median of 30, and a maximum of 40?





        

4.2 Six statistical scores are 70, 60, 80, 90, 90, 70. What is the median value of these scores?





        

4.3 There are cards that write each and every one of them as Numbers 1, 2, 3, ... \(n\). What is the average of these numbers?





        

4.4 I bought 10 tomatoes which cost 1 dollar each and 10 tomatoes which cost 2 dollars each. How much is its cost in average for each?





        

4.5 If the averages of two data sets are \(\small \overline x_1\), \(\small \overline x_2\) and their data sizes are \(n_1\), \(n_2\) what is the average of the total data combined?





        

4.6 If data are \(x_1 , x_2 , ... , x_n \) and its mean is \(\small \overline x\), what is the value of \(\small \sum_{i=1}^{n} (x_i - \overline x)\) ?





        

4.7 Which of the following properties of the mean is incorrect?





        

4.8 The following table is the evaluation scores of a university student. What is the weighted average of the scores using the credits as weights?

Course Name A B C D E F
Credit 4 3 3 2 2 1
Score 80 90 85 95 75 90




        

4.9 Which of the following statistical analysis is wrong if the 1st quartile is 68.25 and the 2nd quartile is 79.06 and the 3rd quartile is 90.75?





        

4.10 What is a convenient measure to compare the dispersion of data which has different units?





        

Practice Exercise

*** Answer the followings

4.1 Mid term scores of a Statistics course are 70, 60, 80, 90, 90, 70. What is the mean and the median of this data?

4.2 There are cards that write numbers 1, 2, 3, ... , n. What is the average of these numbers?

4.3 For data measured as 2, 3, 7, 7, 7, 7, 8, find the mean, the median and the mode.

4.4 The following table is the evaluation scores of the courses taken by a student this semester. What is the weighted mean of these scores by using the credits as their weights?

Course Name A B C D
Credit 4 3 3 2
Score 80 90 75 90

4.5 Test scores of 10 students which we sampled from all students of Statistics course were 6, 8, 7, 8, 5, 9, 7, 10, 9, 4. What is the sample mean and the sample standard deviation?

4.6 Life expectancies of 10 different automobiles sampled from a population were investigated as follows: (unit year)

3 3 8 7 4 6 5 2 5 10

Calculate
1) mean, 2) median, 3) mode, 4) variance and standard deviation,
5) coefficient of variation, 6) range, 7) inter-quartile range.

4.7 After sampling 10 employees from a company, we examined commuting distances (km) from their home to the company and found the following data.

3 16 12 11 14 5 7 14 9 8

Calculate
1) mean, 2) median, 3) mode, 4) variance and standard deviation,
5) coefficient of variation, 6) range, 7) inter-quartile range.

4.8 The following is a list of stock prices of a company during the last 25 days of closing. (Unit: US$)

131, 135, 129, 123, 130, 136, 134, 140, 146, 150,
153, 150, 148, 151, 153, 158, 161, 165, 160, 155,
157, 163, 159, 160, 160.

Use 『eStat』 to do the followings.
1) Calculate the mean, the median and the mode for the above data.
2) Obtain the weighted average by weighting 25 on the stock price of the most recent work, then 24 on the next stock price, ... and 1 on the stock price of the first date. Compare the mean value obtained in 1) with that value.
3) Calculate the variance and the standard deviation, the coefficient of variation, the range, the inter-quartile range.
4) Calculate the 1st quartile (Q1) and the 3rd quartile (Q3).
5) Draw a box plot.

4.9 Scores of two bowling players playing 10 games were as follows.

Player A Player B
198 196
119 159
174 162
235 178
134 188
192 169
124 173
241 183
158 177
176 152

Use 『eStat』 to do the followings.
1) Calculate the mean and the median for each player.
2) Find the standard deviation, the range, the 1st quartile, the 3rd quartile and the inter-quartile range for each player.
3) Draw a box plot.
4) Who do you think is the better player? Why?

4.10 To test the effectiveness of a memory improvement technique developed by a psychologist, 30 samples observed the difference in time taken to memorize 10 numerical sequences of 10 pairs before and after learning the technique, as shown below. (Unit: Minutes)

5, 10, 15, 11, 13, 20, 14, 5, 23, 18, 17, 4, 19, 5, 24, 18, 15, 21,
24, 16, 2, 15, 19, 22, 24, 21, 14, 18, 26, 10

Use 『eStat』 to do the followings.
1) Draw a histogram of the above data. Find the frequency table of the histogram.
2) Calculate the mean and the median and compare their values.
3) Calculate the quartiles and draw a box plot.