The table below shows the distribution of the number of public library cards owned by a group of families in a certain neighborhood. | Number of library cards | Number of families | |---|---| | 1 | 4 | | 2 | 5 | | 3 | 2 | | 4 | 1 | What is the median number of public library cards owned by these fam

The table below shows the distribution of the number of public library cards owned by a gr… — SAT

The table below shows the distribution of the number of public library cards owned by a group of families in a certain neighborhood.

What is the median number of public library cards owned by these families?

Answer: 2

The median number of public library cards is 2.

To find the median, first determine the total number of families by summing the frequencies:

4 + 5 + 2 + 1 = 12

. Since the number of data points is even, the median is the average of the two middle values (

6^{\text{th}}

and

7^{\text{th}}

values). Sorting the data, the first 4 values are 1, and the next 5 values (positions 5 through 9) are 2. Since both the

6^{\text{th}}

and

7^{\text{th}}

values are 2, the median is 2.

Find the total number of families by adding the frequencies.

4 + 5 + 2 + 1 = 12

To determine the position of the median in the dataset, we must first find the total number of data points.

Identify the positions of the middle values.

The

6^{\text{th}}

and

7^{\text{th}}

values.

For an even number of data points (

n = 12

), the median is the average of the values at positions

\frac{n}{2}

and

\frac{n}{2} + 1

Find the values at the

6^{\text{th}}

and

7^{\text{th}}

positions using the frequency table.

Both the

6^{\text{th}}

and

7^{\text{th}}

values are 2.

Accumulating the frequencies from top to bottom: the first 4 values are 1, and the next 5 values (positions 5 to 9) are 2.

Calculate the average of the two middle values.

\frac{2 + 2}{2} = 2

The median of an even-sized dataset is the arithmetic mean of its two middle values.

Calculating the median from a frequency table