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# The following data represent the​ high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts​ (a) through​ (c).Temperature Lower Limit Upper Limit Days50-59                50                    59            260-69                60                    69          31370-79                 70                    79         141980-89                80                    89         150390-99                90                    99          319100-109            100                  109            9 ​(a) Approximate the mean and standard deviation for temperature.

Question
The following data represent the​ high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts​ (a) through​ (c).
Temperature Lower Limit Upper Limit Days
50-59                50                    59            2
60-69                60                    69          313
70-79                 70                    79         1419
80-89                80                    89         1503
90-99                90                    99          319
100-109            100                  109            9

​(a) Approximate the mean and standard deviation for temperature.
check_circleAnswer
Step 1

Here, first lower case and upper case limits are 50 and 59. Then, the midpoint of the class is 54.5 (=(50+59)/2); so x1 is 54.5. Similarly, calculate the midpoints for the remaining classes.

Step 2

The values of ∑fi, ∑fixi and ∑fixi2 are calculated as follows:

Step 3

The mean for temperature is ...

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