Question

choose the best answer.

use this data set for 1 and 2.
5, 4, 6, 3, 1, 4, 4

1. find the mean, median, and mode of the data set.

a 3, 4, 5 c 4, 3.9, 4
b 4, 4, 4 d 3.9, 4, 4

1. what are the mean and median of this data set without the value 1?

a 4.3, 4 b 4, 4.3

use this data set for 3 and 4.
7, 13, 9, 15, 11, 7, 11

1. find the interquartile range.

a 11 c 7
b 6 d 13

1. which is the correct box-and-whisker plot for the data set?

a, b, c, d box-and-whisker plots on number lines

1. find the mean absolute deviation for this data set.

2, 3, 1, 5, 4
a 2.1 c 2
b 1 d 1.2

1. which data set does the line plot represent?

line plot with xs at 1, 3, 4, 6, 7, 8
a 1,1,2,3,3,3,4,6,6,7,7,8,8,8
b 1,1,2,3,3,4,6,6,6,7,7,8,8,8
c 1,1,3,3,3,4,5,6,6,7,7,8,8,8
d 1,1,3,3,3,4,6,6,6,7,7,8,8,8

1. the data set and dot plot display the number of questions a student missed on 10 math quizzes. what is a correct description of the distribution?

table: 3, 0, 2, 3, 6; 2, 4, 3, 3, 4
dot plot: 0(1), 2(2), 3(4), 4(2), 6(1)
a the data is skewed; the measures of center are varied.
b the data is skewed; the measures of center are equal.
c the data is normal; the measures of center are varied.
d the data is normal; the measures of center are equal.

Explanation:

Question 1

Step1: Calculate the mean

The data set is \(5, 4, 6, 3, 1, 4, 4\). The sum of the data is \(5 + 4 + 6 + 3 + 1 + 4 + 4 = 27\). There are 7 data points. So the mean is \(\frac{27}{7}\approx 3.9\).

Step2: Find the median

First, order the data: \(1, 3, 4, 4, 4, 5, 6\). The middle value (4th term) is 4, so the median is 4.

Step3: Determine the mode

The number 4 appears most frequently (3 times), so the mode is 4.

Step1: New data set (without 1)

The new data set is \(5, 4, 6, 3, 4, 4\). The sum is \(5 + 4 + 6 + 3 + 4 + 4 = 26\). There are 6 data points. Mean is \(\frac{26}{6}\approx 4.3\).

Step2: Find the median

Order the data: \(3, 4, 4, 4, 5, 6\). The middle values are the 3rd and 4th terms (both 4), so median is \(\frac{4 + 4}{2}= 4\).

Step1: Order the data

Data set: \(7, 13, 9, 15, 11, 7, 11\) ordered is \(7, 7, 9, 11, 11, 13, 15\).

Step2: Find Q1 and Q3

The median (middle term) is 11 (4th term). The lower half is \(7, 7, 9\), Q1 is the median of the lower half, which is 7. The upper half is \(11, 13, 15\), Q3 is the median of the upper half, which is 13.

Step3: Calculate IQR

IQR = Q3 - Q1 = \(13 - 7 = 6\).

Answer:

D (3.9, 4, 4)

Question 2