Question

use each students quiz score to answer the questions. annikas quiz scores 60%, 75%, 78%, 80%, 85%, 85%, 90% josiahs quiz scores 62%, 65%, 68%, 79%, 83%, 90%, 92% annika has a mean that is josiahs mean. josiahs median is annikas median. the range is . who has the lowest interquartile range? annika josiah they had the same interquartile range.

Explanation:

Step1: Calculate Annika's mean

$\text{Mean}=\frac{60 + 75+78 + 80+85+85+90}{7}=\frac{553}{7}=79$

Step2: Calculate Josiah's mean

$\text{Mean}=\frac{62 + 65+68+79+83+90+92}{7}=\frac{539}{7}=77$

Step3: Compare means

Annika's mean ($79$) is greater than Josiah's mean ($77$)

Step4: Find Annika's median

The data set has 7 values. The median is the 4 - th value when ordered. Annika's median is $80$

Step5: Find Josiah's median

The data set has 7 values. The median is the 4 - th value when ordered. Josiah's median is $79$
Josiah's median ($79$) is less than Annika's median ($80$)

Step6: Calculate Annika's range

$\text{Range}=90 - 60=30$

Step7: Calculate Josiah's range

$\text{Range}=92 - 62 = 30$
The ranges are equal

Step8: Calculate Annika's inter - quartile range

First, find the lower half ($60,75,78$) and upper half ($85,85,90$) of the data. The first quartile $Q_1$ is the median of the lower half, $Q_1 = 75$. The third quartile $Q_3$ is the median of the upper half, $Q_3=85$. $\text{IQR}=Q_3 - Q_1=85 - 75 = 10$

Step9: Calculate Josiah's inter - quartile range

First, find the lower half ($62,65,68$) and upper half ($90,92,83$). The first quartile $Q_1$ is the median of the lower half, $Q_1 = 65$. The third quartile $Q_3$ is the median of the upper half, $Q_3=90$. $\text{IQR}=Q_3 - Q_1=90 - 65 = 25$
Annika has the lowest inter - quartile range

Answer:

Annika has a mean that is greater than Josiah's mean.
Josiah's median is less than Annika's median.
The range is the same for both.
Annika has the lowest interquartile range.