You are viewing the article Question Video: Calculating Upper and Lower Quartiles for a Set of Data at **Lassho.edu.vn** you can quickly access the necessary information in the table of contents of the article below.

### Video Transcript

David’s history test scores are 74,

96, 85, 90, 71, and 98. Determine the upper and lower

quartiles of his scores.

In order to calculate the upper and

lower quartiles for a data set, we firstly need to sort the data into ascending

order. In this case, the lowest score was

71. The next lowest score was 74. The remainder of David’s scores in

ascending order were 85, 90, 96, and 98. We have six test scores in total,

and we know that the median is the middle value.

One way to calculate the median

with a small data set is to cross off numbers from either end. We cross off the smallest number

and the largest number. We then cross off 74 and 96. This means we’re left with two

middle numbers, 85 and 90. The median will be the midpoint of

these two numbers. We could work this out on a number

line. Alternatively, we can find the

average or midpoint of two numbers by finding their sum and dividing by two. This is equal to 87.5. The median of David’s test scores

is 87.5.

An alternative way of finding the

median, which is useful if we have a large data set, is by using the formula 𝑛 plus

one divided by two. This gives us the median position

on the list. As there were six values in this

question, 𝑛 is equal to six. Six plus one is equal to seven, and

dividing by two gives us 3.5. This means that the median will be

halfway between the third and fourth value. This confirms that our answer of

87.5 was correct.

As we had six values in total,

there are three values less than the median and three values greater than the

median. We know that the lower quartile is

the center of the bottom half of our data set. As there are three values here, the

lower quartile, or Q one, will be the middle one. This is equal to 74. The upper quartile will be the

center of the top half of our data set. Once again, we have three numbers

above the median. The center number will be the

middle one. This is equal to 96.

We can therefore conclude that the

upper quartile of David’s history scores was 96 and the lower quartile was 74. Before moving on from this

question, let’s consider how we could find the lower quartile and upper quartile

position. The position of the lower quartile

can be calculated using the formula 𝑛 plus one divided by four or a quarter of 𝑛

plus one. Seven divided by four is equal to

1.75. As this is more than halfway

between one and two, we round up to two. The lower quartile will be the

second value in our list.

We can calculate the position of

the upper quartile using a similar method. Three-quarters of 𝑛 plus one, or

three multiplied by 𝑛 plus one divided by four. This is equal to 5.25, which we

notice is three times 1.75. As this is less than halfway

between five and six, we round down to five. The fifth number in our list will

be the upper quartile. This method is particularly useful

if we have a large data set.

Thank you for reading this post Question Video: Calculating Upper and Lower Quartiles for a Set of Data at **Lassho.edu.vn** You can comment, see more related articles below and hope to help you with interesting information.

**Related Search:**