Question

1 the data set represents the number of errors on a typing test. 5 6 8 8 9 9 10 10 10 12 a. what is the median? 9 interpret this value in the situation. b. what is the iqr? 2 the data set represents the heights, in centimeters, of 10 model bridges made for an engineering competition. 13 14 14 16 16 16 16 18 18 19 a. what is the mean? b. what is the mad? 3 from unit 1, lesson 4 describe the shape of the distribution shown in the dot - plot. the dot plot displays the golf scores from a golf tournament.

Explanation:

1.

a.

Step1: Arrange data in order

$5,6,8,8,9,9,10,10,10,12$

Step2: Find median position

There are $n = 10$ data - points. The median position is $\frac{n + 1}{2}=\frac{10+1}{2}=5.5$. So, the median is the average of the 5th and 6th ordered values.

Step3: Calculate median

Median$=\frac{9 + 9}{2}=9$.
Interpretation: Half of the typing - test results have 9 or fewer errors, and half have 9 or more errors.

Step1: Find the lower half and upper half

The lower half of the data $5,6,8,8,9$ has a median (first - quartile $Q_1$) of 8. The upper half of the data $9,10,10,10,12$ has a median (third - quartile $Q_3$) of 10.

Step2: Calculate the IQR

IQR$=Q_3−Q_1=10 - 8=2$.

Step1: Use the mean formula

The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$, where $n = 10$ and $x_i$ are the data - points $13,14,14,16,16,16,16,18,18,19$.

Step2: Calculate the sum

$\sum_{i=1}^{10}x_i=13 + 14+14+16+16+16+16+18+18+19=158$.

Step3: Calculate the mean

$\bar{x}=\frac{158}{10}=15.8$.

Answer:

9

b.