Central Limit Theorem Worksheet

**Page 1**

1.

Which is not part of the five-number summary?

I. Q_{1} and Q_{3}

II. The mean

III. The median

IV. The smallest and largest data values

I. Q

II. The mean

III. The median

IV. The smallest and largest data values

a. | III only | ||

b. | I only | ||

c. | IV only | ||

d. | II only |

The lowest value of the data set, Q

These values are called a five-number summary of the data set.

So, out of 4 choices the mean is not present in the five number summary of the data set.

Correct answer : (4)

2.

Which of the following box plots represents the number of calculators sold during a randomly selected week?

8, 12, 23, 5, 9, 15, 3.

a. | Figure 4 | ||

b. | Figure 2 | ||

c. | Figure 1 | ||

d. | Figure 3 |

The median of the above data is 9.

Q

[Q

Q

[Q

Draw a box around Q

Correct answer : (3)

3.

P_{50} corresponds to ____.

I. Q_{2}

II. IQR

III. MR

IV. D_{5}

I. Q

II. IQR

III. MR

IV. D

a. | II and IV only | ||

b. | II and III only | ||

c. | I only | ||

d. | I and IV only |

So, P

Quartiles are denoted by Q

So, P

But IQR = Q

So, P

So, P

Correct answer : (4)

4.

Which of the following statement(s) is/are true?

I. If a student secured 75th percentile in an exam, then it means that he scored 75 out of 100.

II. A statistic that tells the number of standard deviations a data value is above or below the mean is called $z$ score.

III. The distribution is positively skewed if the mode is to the left of the median and the mean is to the right of the median.

I. If a student secured 75th percentile in an exam, then it means that he scored 75 out of 100.

II. A statistic that tells the number of standard deviations a data value is above or below the mean is called $z$ score.

III. The distribution is positively skewed if the mode is to the left of the median and the mean is to the right of the median.

a. | III only | ||

b. | II and III only | ||

c. | II only | ||

d. | I, II and III only |

If a student's score corresponds to 75

The

The distribution is positively skewed if the mode is to the left of the median and the mean is to the right of the median.

So, only statements II and III are true.

Correct answer : (2)

5.

Identify the five-number summary for the number of previous jobs held by each of six job applicants for clerk's post to BRR company if the number of jobs data is given as 2, 4, 5, 6, 8, 9.

a. | 4, 5.5, 8, 4 | ||

b. | 2, 4, 5.5, 8, 9 | ||

c. | 2, 4, 8, 9, 4 | ||

d. | 2, 4, 5.5, 8, 9, 4 |

Lowest value of given data set is 2.

Highest value of given data set is 9.

Median = Q

Q

[Q

Q

[Q

So, five-number summary of the given data set is 2, 4, 5.5, 8, 9.

Correct answer : (2)

6.

Which of the following statement(s) is/are true ?

I. Mode is the measure of central tendency used in exploratory data analysis (EDA).

II. Extremely low data value in the data set can be considered as an outlier.

III. Percentiles are the same as percentages.

I. Mode is the measure of central tendency used in exploratory data analysis (EDA).

II. Extremely low data value in the data set can be considered as an outlier.

III. Percentiles are the same as percentages.

a. | II only | ||

b. | I, II and III only | ||

c. | II and III only | ||

d. | I and III only |

An outlier is an extremely high or an extremely low data value when compared with the rest of the data values in the data set.

Percentile =

So, percentiles are position measures to indicate the position of an individual in a group.

Correct answer : (1)

7.

Recognize the incorrect statement(s).

I. When all data for a variable are transformed into $z$ scores, the resulting distribution will have a mean of 1 and a standard deviation of 0.

II. The $z$ score represents the number of standard deviations that a data value falls above or below the mean.

III. Percentages are position measures used to compare the relative position of an individual in a group.

IV. Percentile divide the data set into 100 equal groups.

I. When all data for a variable are transformed into $z$ scores, the resulting distribution will have a mean of 1 and a standard deviation of 0.

II. The $z$ score represents the number of standard deviations that a data value falls above or below the mean.

III. Percentages are position measures used to compare the relative position of an individual in a group.

IV. Percentile divide the data set into 100 equal groups.

a. | I only | ||

b. | I and III only | ||

c. | II and IV only | ||

d. | IV only |

The

Percentiles are position measures used to compare the relative position of an individual in a group. (Percentile is not same as percentage.)

Percentile divide the data set into 100 equal groups.

Therefore, statements I and III are incorrect.

Correct answer : (2)

8.

The time (in minutes) taken by Moore and James to swim 2000 yards for 8 sessions in a pool are given.

Compare the distributions using box plots.

Moore | James |

34.02 | 36.12 |

34.12 | 35.37 |

35.72 | 35.57 |

34.72 | 35.43 |

34.05 | 36.05 |

34.13 | 34.85 |

36.17 | 34.75 |

36.07 | 34.18 |

a. | Both median and variation is higher and larger for James. | ||

b. | Both median and variation is higher and larger for Moore. | ||

c. | Median is higher for the distribution of James & variation is larger for the distribution of Moore. | ||

d. | Median is higher for the distribution of Moore & variation is larger for the distribution of James. |

Q

Q

Q

Arrange the data in order for James: 34.18, 34.75, 34.85, 35.37, 35.43, 35.57, 36.05, 36.12

Q

Q

Q

Draw the box plots for each distribution on the same graph.

From the box plots, the distribution of time slot for James has higher median than for Moore. The variation or spread for the distribution of time slot for Moore is larger than the variation for James.

Correct answer : (3)

9.

The owner of a restaurant recorded the number of visitors for a period of one week. Examine the nature of distribution of the data, using a box plot. 256, 542, 340, 460, 380, 429, 412

a. | symmetric | ||

b. | positively skewed | ||

c. | negatively skewed | ||

d. | approximately symmetric |

Q

[Q

Q

[Q

Q

[Q

Draw a graph for the data and locate Q

Since the correct median falls to the right of the center, the distribution is negatively skewed.

Correct answer : (3)

10.

The median price of different books in a bookstall is $35.The difference between twice the minimum price and half the maximum price in the bookstall gives the median price, which is also equal to the midrange. The IQR of the prices is $5. The price of the book corresponding to 25th percentile is $32. Identify five - number summary .

a. | 28, 32, 35, 37, 42 | ||

b. | 28, 42, 32, 35, 37 | ||

c. | 28, 37, 42 | ||

d. | 12, 24, 35, 40, 56 |

2

4

[Given median = 35.]

2

[Given median = midrange.]

4

3

Solve (1) and (2)

8

3

____________

5

If

[From step 2, 3

So, the minimum price in the book stall is 28 and maximum price in the book stall is 42.

The price of the book corresponding to 25

So, Q

[Q

Q

Q

[Given IQR = 5.]

The five - number summary is 28, 32, 35, 37, 42.

Correct answer : (1)