Question

The data set represents the number of cars in a town given a speeding ticket each day for 10 days

2, 4, 5, 5, 7, 7, 8, 8, 8, 12
a. What is the median? Interpret this value in the situation.
b. What is the IQR?

if possible can anyone help me with the entire first page it’s for finals

Answer 1

I can help you with the first part. Let's start with the median.

a. **Median:**
To find the median, you need to arrange the data in ascending order:
2, 4, 5, 5, 7, 7, 8, 8, 8, 12

Since there are 10 observations, the median will be the average of the 5th and 6th values, which are both 7.

So, the median is 7. In the context of the number of cars receiving speeding tickets each day, this means that half of the days had 7 or fewer cars, while the other half had 7 or more.

For part b, I'll calculate the Interquartile Range (IQR):

b. **Interquartile Range (IQR):**
1. Find the first quartile (Q1) - the median of the lower half of the data.
2. Find the third quartile (Q3) - the median of the upper half of the data.
3. Calculate IQR as \(Q3 - Q1\).

Let's find Q1 and Q3:
\[Q1 = \frac{4 + 5}{2} = 4.5\]
\[Q3 = \frac{8 + 8}{2} = 8\]

Now, calculate the IQR: \(IQR = Q3 - Q1 = 8 - 4.5 = 3.5\)

So, the Interquartile Range (IQR) is 3.5. This measure helps describe the spread of the middle 50% of the data, giving you an idea of how concentrated or dispersed the values are within that range.