The table below shows the daily high temperatures, in degrees Celsius, recorded in a city over a 9-day period. | Daily High Temperature (°C) | Number of Days | | :---: | :---: | | 18 | 3 | | 19 | 1 | | 20 | 2 | | 21 | 3 | Based on the table, what was the median daily high temperature, in degrees Cel

The table below shows the daily high temperatures, in degrees Celsius, recorded in a city … — SAT

The table below shows the daily high temperatures, in degrees Celsius, recorded in a city over a $9$ -day period.

Based on the table, what was the median daily high temperature, in degrees Celsius, for the $9$ -day period?

Answer: 20 °C

The median daily high temperature for the 9-day period is

20

°C.

To find the median daily high temperature, we first sum the frequencies to find the total number of days:

3 + 1 + 2 + 3 = 9

. Because

9

is an odd number, the median is the middle value, which is the

5

th value when the data points are ordered from least to greatest. The first

3

values are

18

, the

4

th value is

19

, and the

5

th and

6

th values are

20

. Therefore, the

5

th value in the ordered list is

20

Determine the total number of observations (days) in the data set.

9

days

To find the position of the median value, we must first calculate the total number of data points by adding the frequencies:

3 + 1 + 2 + 3 = 9

Find the position of the median in the ordered data set.

5

th position

For an odd number of observations

n

, the median is located at the

\frac{n+1}{2}

position. With

n = 9

, this corresponds to the

\frac{9+1}{2} = 5

th value.

Identify the temperature at the

5

th position using the frequency table.

20

Listing the temperatures in ascending order gives:

18, 18, 18

(positions 1–3),

19

(position 4), and

20, 20

(positions 5–6). The value at the

5

th position is

20

Finding the median of a frequency distribution