Question

1. You are a fifth-grade teacher and have just given your students a spelling test. Their scores on the test are as follows: 100, 98,25,30, 100, 100, 20, 100, 100, 99, 97, 96, 20. Calculate the mean for these scores. Do you think it reflects the scores adequately? Explain your answer.

2. Calculate means, medians, and modes for the following 2 sets of scores: Set 1: 100, 20, 100, 98, 100, 99, 100, 100 Set 2: 100, 100, 20 Based on your calculations, what TWO important observations can you make about the effect of extreme scores on the mean?

3. What is a frequency distribution?

4. What are the measures of central tendency? Explain.

5. Describe what a negatively skewed distribution (or frequency polygon) looks like and why it does not look like a normal distribution.

Answer 1

Solution:

It is not reflects the scores adequately because 75.77 is not match any value of spelling test score of any students and there are some outliers in data therefore mean is not giving good result. when outliers present in the data, so the mean does not give better result.

Set 1:

100, 20, 100, 98, 100, 99, 100, 100

Now find the Mean:

Now find the Median:

When calculating the median then first arrange the value in ascending order.

20,98,99,100,100,100,100,100

n = 8 when n is even then use this formula to calculate the median:

See 4th therm and 5th term in step 1 data:

Now find the Mode:

See the most frequent value in the data and 100 value is the most frequent value.

Set 2 :

100, 100, 20

Now find the Median:

20,100,100

n = 3 when n is odd then use this formula to calculate the Median:

See the 2nd value in Set 2:

Now find the Mode:

Mode = 100

Mean and Median is giving good result from Mean.

Frequency distribution:

A frequency distribution is the value of each data present they how much frequent.

like see Set 2: 20 frequency is one and 100 frequency is 2.

Measures of central tendency:

Measures of central tendency is use for to find the location of the central point and the most use for central tendency is mean, median and mode.

Negatively skewed distribution: