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Between which two values would 50 of the data lie?

Fifty percent of the data values lies between 34 and 46. 2.

Which values are used in a box plot?

A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value.

What does the box portion of a Boxplot display?

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.

What is the 5 number summary in stats?

A five-number summary is especially useful in descriptive analyses or during the preliminary investigation of a large data set. A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.

What are the 5 numbers in the five number summary?

The key values are called a five-number summary, which consists of the minimum, first quartile, median, second quartile, and maximum.

How do you find the five point summary?

How to Find a Five-Number Summary: Steps

  1. Step 1: Put your numbers in ascending order (from smallest to largest).
  2. Step 2: Find the minimum and maximum for your data set.
  3. Step 3: Find the median.
  4. Step 4: Place parentheses around the numbers above and below the median.
  5. Step 5: Find Q1 and Q3.

How do you find Q1 Q2 and Q3 in statistics?

In this case all the quartiles are between numbers:

  1. Quartile 1 (Q1) = (4+4)/2 = 4.
  2. Quartile 2 (Q2) = (10+11)/2 = 10.5.
  3. Quartile 3 (Q3) = (14+16)/2 = 15.

How do you find Q1 and Q3 from mean and standard deviation?

Quartiles: The first and third quartiles can be found using the mean µ and the standard deviation σ. Q1 = µ − (. 675)σ and Q3 = µ + (. 675)σ.

What is the formula for Q1 and Q3?

Q1 is the middle value in the first half of the data set. Since there are an even number of data points in the first half of the data set, the middle value is the average of the two middle values; that is, Q1 = (3 + 4)/2 or Q1 = 3.5. Q3 is the middle value in the second half of the data set.

How do you find the upper quartile on a calculator?

How to Calculate Quartiles

  1. Order your data set from lowest to highest values.
  2. Find the median. This is the second quartile Q2.
  3. At Q2 split the ordered data set into two halves.
  4. The lower quartile Q1 is the median of the lower half of the data.
  5. The upper quartile Q3 is the median of the upper half of the data.

How do you find the interquartile range on a calculator?

This simple tool works out the interquartile range of a set of numbers by calculating the 25th and 75th percentiles, and then subtracting the former from the latter (i.e., IQR = Q3 – Q1). Enter your data into the text box below, and then hit the “Calculate Percentile” button.

What is the IQR rule?

A commonly used rule says that a data point is an outlier if it is more than 1.5 ⋅ IQR 1.5/cdot /text{IQR} 1. 5⋅IQR1, point, 5, dot, start text, I, Q, R, end text above the third quartile or below the first quartile.

How do you find the interquartile range of a normal distribution?

When working with box plots, the IQR is computed by subtracting the first quartile from the third quartile. In a standard normal distribution (with mean 0 and standard deviation 1), the first and third quartiles are located at -0.67448 and +0.67448 respectively. Thus the interquartile range (IQR) is 1.34896.

What does the Iqr tell you about the data?

The IQR tells how spread out the “middle” values are; it can also be used to tell when some of the other values are “too far” from the central value. These “too far away” points are called “outliers”, because they “lie outside” the range in which we expect them.

Why do we use interquartile range?

The IQR is used to measure how spread out the data points in a set are from the mean of the data set. It is best used with other measurements such as the median and total range to build a complete picture of a data set’s tendency to cluster around its mean.

What is the 1.5 IQR rule?

Add 1.5 x (IQR) to the third quartile. Any number greater than this is a suspected outlier. Subtract 1.5 x (IQR) from the first quartile. Any number less than this is a suspected outlier.

What if the IQR is zero?

Having an IQR of 0 means there is no variability in the middle 50% of your data, but the center of the distribution can be anywhere. In this case, values greater than the 75th percentile are dragging your mean up to a value greater than the 75th percentile.

Can the Iqr be negative?

You’re just taking the difference of the two quartiles, which can contain negative numbers because it is at the interval level. The IQR cannot be negative because you subtract the larger quartile from the smaller one, always resulting positive, even with negative numbers. It is a range, so it has to be positive.

How do you report Iqr?

Interquartile range is a range, so a difference between third and first quartiles IQR = Q3 – Q1. So it is a single number statistic, so this is exactly how you report it.

How is quartile calculated?

The quartile measures the spread of values above and below the mean by dividing the distribution into four groups. A quartile divides data into three points—a lower quartile, median, and upper quartile—to form four groups of the dataset.

What is the formula for lower quartile?

If there are (4n+3) data points, then the lower quartile is 75% of the (n+1)th data value plus 25% of the (n+2)th data value; the upper quartile is 25% of the (3n+2)th data point plus 75% of the (3n+3)th data point.

Is the First Quartile the same as the 25th percentile?

The first quartile, Q1 , is the same as the 25 th percentile, and the third quartile, Q3 , is the same as the 75 th percentile. The median, M , is called both the second quartile and the 50 th percentile.

What do quartiles tell us?

Quartiles tell us about the spread of a data set by breaking the data set into quarters, just like the median breaks it in half. For example, consider the marks of the 100 students below, which have been ordered from the lowest to the highest scores, and the quartiles highlighted in red.

What does the upper quartile tell us?

The upper quartile is the median of the upper half of a data set. This is located by dividing the data set with the median and then dividing the upper half that remains with the median again, this median of the upper half being the upper quartile. N represents the number of elements in the data set.

What is the importance of quartile?

Quartiles are great for reporting on a set of data and for making box and whisker plots. Quartiles are especially useful when you’re working with data that isn’t symmetrically distributed, or a data set that has outliers.

What does the first quartile tell you?

The first quartile or Q1 is the value in the data set such that 25% of the data points are less than this value and 75% of the data set is greater than this value.

What are the uses of quartile deviation?

The quartile deviation helps to examine the spread of a distribution about a measure of its central tendency, usually the mean or the average. Hence, it is in use to give you an idea about the range within which the central 50% of your sample data lies.