The number of foreign workers’ certificates for the New...

The number of foreign workers’ certificates for the New England states and the northwestern states is shown. Find the mean, median, and mode for both areas and compare the results. New England states $\quad$Northwestern states $\begin{array}{ccc}{6768} & {1870} \\ {3196} & {622} \\ {1112} & {620} \\ {819} & {23} \\ {1019} & {172} \\ {1795} & {112}\end{array}$

The number of foreign workers’ certificates for the New England states and the northwestern states is shown. Find the mean, median, and mode for both areas and compare the results.
New England states $\quad$Northwestern states
$\begin{array}{ccc}{6768} & {1870} \\ {3196} & {622} \\ {1112} & {620} \\ {819} & {23} \\ {1019} & {172} \\ {1795} & {112}\end{array}$

Key Concepts

Mean

The mean is an arithmetic average derived by summing all the numbers in a dataset and dividing by the total count of numbers. It provides a measure of central tendency that reflects the overall level of the data, though it can be influenced by extremely high or low values.

Median

The median is the middle value in an ordered dataset, dividing the data into two equal halves. This measure of central tendency is particularly useful for understanding the central position of the data, especially when the dataset contains outliers or is skewed.

Mode

The mode is the value that appears most frequently in a dataset. As a measure of central tendency, it is useful for identifying the most common or typical value within the data and is especially informative when data values repeat.

Comparison of Distributions

Comparing the mean, median, and mode across different datasets allows for an analysis of their distribution characteristics, including symmetry, skewness, and the presence of outliers. This comparative analysis helps in understanding the consistency and variability within each dataset.

Transcript

00:01 The number of foreign workers certificates for the new england states and the northwestern states is shown here.

00:09 Find the mean, median, and mode for both areas and compare the results.

00:16 Okay, the very first thing that you have to do is put them in order from smallest to largest.

00:22 That's for the median.

00:24 So, i went ahead and did that before i started.

00:26 So, first of all, it asked me to find the mean.

00:31 The mean is simply the average.

00:35 So, to find the average, you know, you add them up and divide by how many there are.

00:40 So, for the new england states, i'm taking 819 plus 1019 plus 1112 plus 1795 plus 3196 plus 6768 equals 14 ,709.

01:19 And i'm going to divide that by 6 and i get 2451 .5.

01:35 Alright, let's go ahead and do the northwestern states.

01:39 I'm taking 23 plus 112 plus 172 plus 620 plus 622 plus 1870 equals 3419.

02:08 And divide that by 6 and you get 569 .83 rounded.

02:31 Okay, so there's the mean.

02:33 The median is the one in the middle.

02:36 That's the reason you have to put them in order from smallest to largest.

02:40 When you have an even number of numbers, you're going to have 2 in the middle.

02:46 So, we're going to take the 2 in the middle and add them up and divide by 2.

02:53 So, for the new england states, the 2 in the middle is 1112.

03:01 So, i'm taking 1112 plus 1795 equals, divided by 2, equals 1453 .5.

03:20 And like i said, i got that by taking these 2, adding them together, and then dividing by 2...

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