I am confused on Question 3, page 189 (the topic is Measures of Central Tendency and Variability). I checked the solution and how you formed the equation

87m + 93 = 89(m+1)

But I still do not understand why 89(m+1) is there.

Hi, thanks for the question and apologies for taking a few days to respond. The question tells you that the average peak temperature for the first *m* days of the month was 87 degrees, and that when the next day had a high of 93 degrees, the average peak temperature for the month became 89 degrees.

The key to getting this one is understanding that there are two different ways to calculate the sum of the temperature values. First, you know the average for *m* days was 87 degrees, so you can say the sum of the temperature values for those *m* days was 87*m*. You know the next day was 93 degrees, so the sum of the first *m* days plus the next day is 87*m* + 93. From your question, seems like this is the part you’re good on.

The *other* way to calculate the sum of the temperature values is to multiply the new average you’re told (89 degrees) by the new number of days (*m* + 1). That’s where the 89(*m* + 1) comes from.

Critically, those two ways to calculate the sum must be equal. That allows you to set up the equation 87*m* + 93 = 89(*m* + 1) and solve for *m*.

Does that help?