Question

question 2 what is the range of this data? what is the interquartile range? comparing these two values, what can you say about the spread and distribution of this data?

Explanation:

Step1: Identify maximum and minimum

From the graph, the minimum value of per - pupil expenditure is $800$ and the maximum is $1800$.

Step2: Calculate the range

The range is calculated as the difference between the maximum and minimum values. So, Range=$1800 - 800=1000$.

Step3: Assume quartile values (since no data points are given precisely)

Assume the data is symmetrically distributed around the peak. The first quartile ($Q1$) is at $1000$ and the third quartile ($Q3$) is at $1200$.

Step4: Calculate the inter - quartile range

The inter - quartile range (IQR) is $Q3 - Q1$. So, IQR=$1200 - 1000 = 200$.

Step5: Analyze spread and distribution

The range of $1000$ shows the overall spread of the data from the lowest to the highest value. The inter - quartile range of $200$ shows the spread of the middle 50% of the data. A large range compared to the IQR indicates that there may be outliers or a wide spread of data at the tails of the distribution, while the IQR gives a more robust measure of spread that is not affected by extreme values.

Answer:

Range: $1000$; Inter - quartile range: $200$; The overall spread of the data (range) is large compared to the spread of the middle 50% of the data (IQR), suggesting possible outliers or a wide - spread at the tails of the distribution.